JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
Let \(A\) be a matrix of order \(3 \times 3\) and det \((A)=2\). Then \(\operatorname{det}\left(\operatorname{det}( A )\right.\) adj \(\left(5 \operatorname{adj}\left( A ^{3}\right)\right)\) ) is equal to.....
- A \(512 \times 10^{6}\)
- B \(256 \times 10^{6}\)
- C \(1024 \times 10^{6}\)
- D \(256 \times 10^{11}\)
Answer & Solution
Correct Answer
(A) \(512 \times 10^{6}\)
Step-by-step Solution
Detailed explanation
\(|(\operatorname{det}( A )) \operatorname{adj}(5 \operatorname{adj}( A ))|\) \(=\left|2\, \operatorname{adj}\left(5 \operatorname{adj}\left( A ^{3}\right)\right)\right|\) \(=2^{3} \operatorname{ladj}\left(5 \operatorname{adj}\left( A ^{3}\right) \|\right.\)…
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